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On the relative Morrison-Kawamata cone conjecture (II)
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abstract
Assuming the Morrison-Kawamata cone conjecture for the generic fiber of a Calabi-Yau fibration and the abundance conjecture, we show (1) the finiteness of minimal models, (2) the existence of a weak rational polyhedral fundamental domain under the action of birational automorphism groups, and (3) the finiteness of varieties as targets of contractions. As an application, the finiteness of minimal models and the weak Morrison-Kawamata cone conjecture in relative dimensions $\leq 2$ are established.
Forward citations
Cited by 3 Pith papers
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Boundedness of some fibered K-trivial varieties
Fixed-dimension Calabi-Yau varieties with abelian or primitive symplectic fibrations are birationally bounded, and Lagrangian-fibered primitive symplectic varieties have finitely many deformation classes.
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On the Morrison-Kawamata dream space and its applications
An axiomatic framework (MKD spaces) yields deformation-invariance of divisor cones and a conditional boundedness theorem for rationally connected Calabi–Yau varieties.
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On the boundedness of elliptic Calabi-Yau 4-folds
Elliptic Calabi–Yau 4-folds not crepant to a product quotient of a Calabi–Yau 3-fold times an elliptic curve form a bounded family.
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